Stochastic Finite Element Analysis of Shear-Critical Concrete Structures

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Title: Stochastic Finite Element Analysis of Shear-Critical Concrete Structures

Author(s): Mark D. Hunter, Anca C. Ferche, and Frank J. Vecchio

Publication: Structural Journal

Volume: 118

Issue: 3

Appears on pages(s): 71-83

Keywords: finite element analysis; reinforced concrete; reliability analysis; stochastic simulation

DOI: 10.14359/51730524

Date: 5/1/2021

Abstract:
Stochastic simulation is used primarily as a basis for the resistance models in a reliability analysis, and it is often used to calibrate structural concrete building codes. This paper outlines the implementation of stochastic simulation techniques into a nonlinear finite element analysis framework. The stochastic modeling capabilities implemented include Monte Carlo (MC) sampling and Latin hypercube sampling for uncorrelated uniform sampling, uniform sampling with correlated random variables, and spatial variation using random field generation. Stochastic simulation was conducted for shear-critical beams containing no transverse reinforcement. The simulation results form the basis for a reliability analysis that computes the reliability index for the CSA A23.3-14 code. The calculated reliability index of 2.96 was lower than the target index of 3.5, indicating that the intended performance is not achieved for this type of element. As such, further investigation is required to assess the load factors and safety factors.

Related References:

1. Vecchio, F. J., “Disturbed Stress Field Model for Reinforced Concrete: Formulation,” Journal of Structural Engineering, ASCE, V. 126, No. 9, 2000, pp. 1070-1077. doi: 10.1061/(ASCE)0733-9445(2000)126:9(1070)

2. Nowak, A. S., and Szerszen, M. M., “Calibration of Design Code for Buildings (ACI 318): Part 1—Statistical Models for Resistance,” ACI Structural Journal, V. 100, No. 3, May-June 2003, pp. 378-382.

3. Rakoczy, A., and Nowak, A., “Resistance Model of Lightweight Concrete Members,” ACI Materials Journal, V. 110, No. 1, Jan.-Feb. 2013, pp. 99-109.

4. Bartlett, F. M., “Canadian Standards Association Standard A23.3-04 Resistance Factor for Concrete in Compression,” Canadian Journal of Civil Engineering, V. 34, No. 9, 2007, pp. 1029-1037. doi: 10.1139/l07-034

5. Mirza, S. A.; MacGregor, J. G.; and Hatzinikolas, M., “Statistical Descriptions of Strength of Concrete,” Journal of the Structural Division, V. 105, No. 6, 1979, pp. 1021-1037. doi: 10.1061/JSDEAG.0005161

6. Bartlett, F. M., and MacGregor, J. G., “Statistical Analysis of the Compressive Strength of Concrete in Structures,” ACI Materials Journal, V. 93, No. 2, Mar.-Apr. 1996, pp. 158-168.

7. Unanwa, C., and Mahan, M., “Statistical Analysis of Concrete Compressive Strengths for California Highway Bridges,” Journal of Performance of Constructed Facilities, ASCE, V. 28, No. 1, 2014, pp. 157-167. doi: 10.1061/(ASCE)CF.1943-5509.0000404

8. Habibi, S., “Finite Element Modelling of Corrosion Damaged Reinforced Concrete Structures,” MASc thesis, University of Toronto, 2017.

9. Ferche, A. C.; Panesar, D. K.; Sheikh, S. A.; and Vecchio, F. J., “Toward Macro-Modeling of Alkali-Silica Reaction-Affected Structures,” ACI Structural Journal, V. 114, No. 5, Sept.-Oct. 2017, pp. 1121-1129. doi: 10.14359/51700778

10. Mu, R.; Miao, C.; Luo, X.; and Sun, W., “Interaction between Loading, Freeze–Thaw Cycles, and Chloride Salt Attack of Concrete with and without Steel Fiber Reinforcement,” Cement and Concrete Research, V. 32, No. 7, 2002, pp. 1061-1066. doi: 10.1016/S0008-8846(02)00746-9

11. Ramsay, R. J.; Mirza, S. A.; and MacGregor, J. G., “Monte Carlo Study of Short Time Deflections of Reinforced Concrete Beams,” ACI Journal Proceedings, V. 76, No. 8, 1979, pp. 897-918.

12. Mirza, S. A., and MacGregor, J. G., “Probabilistic Study of Strength of Reinforced Concrete Members,” Canadian Journal of Civil Engineering, V. 9, No. 3, 1982, pp. 431-448. doi: 10.1139/l82-053

13. Mirza, S. A., “Monte Carlo Simulation of Dispersions in Composite Steel-Concrete Conumn Strength Interaction,” Engineering Structures, V. 20, No. 1-2, 1998, pp. 97-104. doi: 10.1016/S0141-0296(97)00049-7

14. Choi, B.; Scanlon, A.; and Johnson, P. A., “Monte Carlo Simulation of Immediate and Time-Dependent Deflections of Reinforced Concrete Beams and Slabs,” ACI Structural Journal, V. 101, No. 5, Sept.-Oct. 2004, pp. 633-641.

15. Vincent, T.; Ozbakkaloglu, T.; Seracino, R.; and Kaggwa, W., “Influence of Variations in Concrete Material Properties on the Serviceability of Reinforced and Prestressed Concrete Flexural Members,” Engineering Structures, V. 33, No. 1, 2011, pp. 99-106. doi: 10.1016/j.engstruct.2010.09.022

16. Ning, C., and Li, B., “Probabilistic Development of Shear Strength Model for Reinforced Concrete Squat Walls,” Earthquake Engineering & Structural Dynamics, V. 46, No. 6, 2017, pp. 877-897. doi: 10.1002/eqe.2834

17. Wong, P. S.; Vecchio, F. J.; and Trommels, H., “VecTor2 & FormWorks User’s Manual,” Technical Report, Department of Civil Engineering, University of Toronto, 2013.

18. Canadian Standards Association, “Design of Concrete Structures (CSA A23.3-14),” CSA, Mississauga, ON, Canada, 2014.

19. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary (ACI 318R-19),” American Concrete Institute, Farmington Hills, MI, 2019, 624 pp.

20. Collins, M. P.; Bentz, E. C.; Quach, P. T.; and Proestos, G. T., “The Challenge of Predicting the Shear Strength of Very Thick Slabs,” Concrete International, V. 37, No. 11, Nov. 2015, pp. 29-37.

21. Melchers, R. E., Structural Reliability Analysis and Prediction, second edition, Wiley, Chichester, UK, 1999.

22. Mirza, S. A., and MacGregor, J. G., “Variability of Mechanical Properties of Reinforcing Bars,” Journal of the Structural Division, V. 105, No. 5, 1979, pp. 921-937. doi: 10.1061/JSDEAG.0005146

23. Graham, C., and Talay, D., Stochastic Simulation and Monte Carlo Methods: Mathematical Foundations of Stochastic Simulation, Springer, New York, 2013.

24. Marsaglia, G., and Tsang, W. W., “A Simple Method for Generating Gamma Variables,” ACM Transactions on Mathematical Software, V. 26, No. 3, 2000, pp. 363-372. doi: 10.1145/358407.358414

25. Hunter, M. D., “Towards Stochastic Finite Element Analysis of Reinforced Concrete Structures,” MASc thesis, University of Toronto, Toronto, ON, Canada, 2016.

26. Mckay, M. D.; Beckman, R. J.; and Conover, W. J., “A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code,” Technometrics, V. 21, No. 2, 1979, pp. 239-245.

27. Olsson, A.; Sandberg, G.; and Dahlblom, O., “On Latin Hypercube Sampling for Structural Reliability Analysis,” Structural Safety, V. 25, No. 1, 2003, pp. 47-68. doi: 10.1016/S0167-4730(02)00039-5

28. Vořechovský, M., and Novák, D., “Simulation of Random Fields for Stochastic Finite Element Analysis,” Proceedings, ICOSSAR, Rotterdam, the Netherlands, 2005, pp. 2545-2552.

29. Choi, S.; Canfield, R. A.; and Grandhi, R. V., “Estimation of Structural Reliability for Gaussian Random Fields,” Structure and Infrastructure Engineering, V. 2, No. 3-4, 2006, pp. 161-173. doi: 10.1080/15732470600590192

30. Vecchio, F. J.; Lai, D.; Shim, W.; and Ng, J., “Disturbed Stress Field Model for Reinforced Concrete: Validation,” Journal of Structural Engineering, ASCE, V. 127, No. 4, 2001, pp. 350-358. doi: 10.1061/(ASCE)0733-9445(2001)127:4(350)

31. Reineck, K.; Bentz, E. C.; Fitik, B. F.; Kuchma, D. A.; and Bayrak, O., “ACI-DAfStb Database of Shear Tests on Slender Reinforced Concrete Beams without Stirrups,” ACI Structural Journal, V. 110, No. 5, Sept.-Oct. 2013, pp. 867-876.

32. Comite Euro-International du Beton, “Model Code for Concrete Structures: CEB-FIP International Recommendations,” third edition, CEB-FIP, Paris, France, 1978, 348 pp.

33. Vecchio, F. J., and Collins, M. P., “The Modified Compression-Field Theory for Reinforced Concrete Elements Subjected to Shear,” ACI Journal Proceedings, V. 83, No. 2, Mar.-Apr. 1986, pp. 219-231.

34. Bentz, E. C., “Sectional Analysis of Reinforced Concrete Members,” doctoral thesis, University of Toronto, Toronto, ON, Canada, 2000.

35. Podgorniak-Stanik, B. A., “The Influence of Concrete Strength, Distribution of Longitudinal Reinforcement, Amount of Transverse Reinforcement, and Member Size on Shear Strength of Reinforced Concrete Members,” master’s thesis, University of Toronto, Toronto, ON, Canada, 1998.

36. Yoshida, Y., “Shear Reinforcement for Large Lightly Reinforced Concrete Members,” master’s thesis, University of Toronto, Toronto, ON, Canada, 2000.

37. Quach, P., “Understanding and Safely Predicting the Shear Response of Large-Scale Reinforced Concrete Structures,” master’s thesis, University of Toronto, Toronto, ON, Canada, 2016.

38. Szerszen, M. M., and Nowak, A. S., “Calibration of Design Code for Buildings (ACI 318): Part 2—Reliability Analysis and Resistance Factors,” ACI Structural Journal, V. 100, No. 3, May-June 2003, pp. 383-391.

39. Nowak, A. S., and Collins, K. R., Reliability of Structures, McGraw Hill, Boston, MA, 2000.

40. Saatci, S., and Vecchio, F. J., “Effects of Shear Mechanisms on Impact Behavior of Reinforced Concrete Beams,” ACI Structural Journal, V. 106, No. 1, Jan.-Feb. 2009, pp. 78-86.

41. Ferche, A. C., and Vecchio, F. J., “Influence of Crack Spacing Parameters on MCFT Calculations of the Behaviour of Shear-Critical Beams without Transverse Reinforcement,” Proceedings, Denis Mitchell Symposium on Developments in Shear and Torsion Design, Seismic Design and Concrete Material, Montreal, QC, Canada, 2017.


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